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Nonresonant Smoothing for Coupled Wave + Transport Equations and the Vlasov-Maxwell System

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Dispersive Transport Equations and Multiscale Models

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 136))

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Abstract

Consider a system (see (1.1) below) consisting of a linear wave equation coupled to a transport equation. Such a system is called nonresonant when the maximum speed for particles governed by the transport equation is less than the propagation speed in the wave equation. Velocity averages of solutions to such nonresonant coupled systems are shown to be more regular than those of either the wave or the transport equation alone. This smoothing mechanism is reminiscent of the proof of existence and uniqueness of C 1 solutions of the Vlasov-Maxwell system by Glassey-Strauss [9] for time intervals on which particle momenta remain uniformly bounded. Applications of our smoothing results to solutions of the Vlasov-Maxwell system are discussed.

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Author information

Authors and Affiliations

  1. C.N.R.S. and D.M.A., Ecole Normale Supérieure, 45 rue d’Ulm, 75230, Paris cedex 05, France

    François Bouchut

  2. Ecole Normale Supérieure, Institut Universitaire de France and D.M.A., 45 rue d’Ulm, 75230, Paris cedex 05, France

    François Golse

  3. Ecole Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235, Cachan Cedex, France

    Christophe Pallard

Authors
  1. François Bouchut
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  2. François Golse
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  3. Christophe Pallard
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Editor information

Editors and Affiliations

  1. Laboratoire MIP, Université Paul Sabatier, Toulouse Cedex 4, 31062, France

    Naoufel Ben Abdallah  & Pierre Degond  & 

  2. Angewandte Mathematik, Universität des Saarlandes, Saarbrucken, D-66041, Germany

    Anton Arnold

  3. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Irene M. Gamba

  4. Department of Mathematics, Indiana University, Bloomington, IN, 47405-5701, USA

    Robert T. Glassey

  5. CSCAMM, University of Maryland, College Park, MD, 20742-4015, USA

    C. David Levermore

  6. Department of Mathematics, Arizona State University, Tempe, AZ, 85287, USA

    Christian Ringhofer

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Bouchut, F., Golse, F., Pallard, C. (2004). Nonresonant Smoothing for Coupled Wave + Transport Equations and the Vlasov-Maxwell System. In: Abdallah, N.B., et al. Dispersive Transport Equations and Multiscale Models. The IMA Volumes in Mathematics and its Applications, vol 136. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8935-2_3

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  • DOI: https://doi.org/10.1007/978-1-4419-8935-2_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6473-6

  • Online ISBN: 978-1-4419-8935-2

  • eBook Packages: Springer Book Archive

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